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Title: Thermally activated post-glitch response of the neutron star inner crust and core. I. Theory

Abstract

Pinning of superfluid vortices is predicted to prevail throughout much of a neutron star. Based on the idea of Alpar et al., I develop a description of the coupling between the solid and liquid components of a neutron star through thermally activated vortex slippage, and calculate the response to a spin glitch. The treatment begins with a derivation of the vortex velocity from the vorticity equations of motion. The activation energy for vortex slippage is obtained from a detailed study of the mechanics and energetics of vortex motion. I show that the 'linear creep' regime introduced by Alpar et al. and invoked in fits to post-glitch response is not realized for physically reasonable parameters, a conclusion that strongly constrains the physics of a post-glitch response through thermal activation. Moreover, a regime of 'superweak pinning', crucial to the theory of Alpar et al. and its extensions, is probably precluded by thermal fluctuations. The theory given here has a robust conclusion that can be tested by observations: for a glitch in the spin rate of magnitude Δν, pinning introduces a delay in the post-glitch response time. The delay time is t{sub d} = 7(t{sub sd}/10{sup 4} yr)((Δν/ν)/10{sup –6}) d, where t{sub sd}more » is the spin-down age; t{sub d} is typically weeks for the Vela pulsar and months in older pulsars, and is independent of the details of vortex pinning. Post-glitch response through thermal activation cannot occur more quickly than this timescale. Quicker components of post-glitch response, as have been observed in some pulsars, notably, the Vela pulsar, cannot be due to thermally activated vortex motion but must represent a different process, such as drag on vortices in regions where there is no pinning. I also derive the mutual friction force for a pinned superfluid at finite temperature for use in other studies of neutron star hydrodynamics.« less

Authors:
 [1]
  1. Department of Physics, Montana State University, Bozeman, MT 59717 (United States)
Publication Date:
OSTI Identifier:
22365677
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 789; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COUPLING; EQUATIONS OF MOTION; HYDRODYNAMICS; LIQUIDS; NEUTRON STARS; NEUTRONS; PULSARS; SPIN; SUPERFLUIDITY; TIME DELAY; VELOCITY; VORTICES

Citation Formats

Link, Bennett, E-mail: link@physics.montana.edu. Thermally activated post-glitch response of the neutron star inner crust and core. I. Theory. United States: N. p., 2014. Web. doi:10.1088/0004-637X/789/2/141.
Link, Bennett, E-mail: link@physics.montana.edu. Thermally activated post-glitch response of the neutron star inner crust and core. I. Theory. United States. doi:10.1088/0004-637X/789/2/141.
Link, Bennett, E-mail: link@physics.montana.edu. Thu . "Thermally activated post-glitch response of the neutron star inner crust and core. I. Theory". United States. doi:10.1088/0004-637X/789/2/141.
@article{osti_22365677,
title = {Thermally activated post-glitch response of the neutron star inner crust and core. I. Theory},
author = {Link, Bennett, E-mail: link@physics.montana.edu},
abstractNote = {Pinning of superfluid vortices is predicted to prevail throughout much of a neutron star. Based on the idea of Alpar et al., I develop a description of the coupling between the solid and liquid components of a neutron star through thermally activated vortex slippage, and calculate the response to a spin glitch. The treatment begins with a derivation of the vortex velocity from the vorticity equations of motion. The activation energy for vortex slippage is obtained from a detailed study of the mechanics and energetics of vortex motion. I show that the 'linear creep' regime introduced by Alpar et al. and invoked in fits to post-glitch response is not realized for physically reasonable parameters, a conclusion that strongly constrains the physics of a post-glitch response through thermal activation. Moreover, a regime of 'superweak pinning', crucial to the theory of Alpar et al. and its extensions, is probably precluded by thermal fluctuations. The theory given here has a robust conclusion that can be tested by observations: for a glitch in the spin rate of magnitude Δν, pinning introduces a delay in the post-glitch response time. The delay time is t{sub d} = 7(t{sub sd}/10{sup 4} yr)((Δν/ν)/10{sup –6}) d, where t{sub sd} is the spin-down age; t{sub d} is typically weeks for the Vela pulsar and months in older pulsars, and is independent of the details of vortex pinning. Post-glitch response through thermal activation cannot occur more quickly than this timescale. Quicker components of post-glitch response, as have been observed in some pulsars, notably, the Vela pulsar, cannot be due to thermally activated vortex motion but must represent a different process, such as drag on vortices in regions where there is no pinning. I also derive the mutual friction force for a pinned superfluid at finite temperature for use in other studies of neutron star hydrodynamics.},
doi = {10.1088/0004-637X/789/2/141},
journal = {Astrophysical Journal},
number = 2,
volume = 789,
place = {United States},
year = {Thu Jul 10 00:00:00 EDT 2014},
month = {Thu Jul 10 00:00:00 EDT 2014}
}
  • A self-consistent quantum approach to describe the inner crust structure of neutron stars is developed within the Wigner-Seitz (WS) approximation, based on the generalized energy functional method involving explicitly neutron and proton pairing correlations. The energy functional is constructed by matching the realistic phenomenological nuclear functional by Fayans et al. for describing the pseudonucleus in the center of the WS cell with the one calculated microscopically for neutron matter within the Brueckner approach with the Argonne v{sub 18} force. The microscopic description of the neutron superfluidity is based on the BCS approach with the same v{sub 18} force. Many-body theorymore » corrections to the BCS method (the correlation and self-energy ones) are included in the calculation scheme in an approximate way. A wide region of average densities was investigated corresponding to the Fermi momentum values k{sub F} = 0.6-1.2 fm{sup -1}.« less
  • Within the Wigner-Seitz approximation, a self-consistent fully quantum-mechanical calculation of the structure of the inner crust of a neutron star is performed over a wide range of densities with allowance for superfluidity effects. Within the approach used, the Wigner-Seitz cell consists of a nuclear-like cluster surrounded by a nearly uniform neutron gas. An effective energy functional is constructed by matching, at the cluster surface, the realistic phenomenological nuclear functional for the cluster due to S.A. Fayans and his coauthors and the energy functional calculated microscopically for neutron matter. The microscopic component of the functional is calculated within the Brueckner methodmore » by using the v18 Argonne interaction.« less
  • A semimicroscopic self-consistent quantum approach was developed recently to describe the inner crust structure of neutron stars within the Wigner-Seitz method and with the explicit inclusion of neutron and proton pairing correlations is used for finding the neutron drip point that separates the outer and inner crusts. The equilibrium configurations of the crust are examined in vicinity of the drip point and in the upper part of the inner crust, for the density region corresponding to average Fermi momenta k{sub F}=0.2 divide 0.5 fm{sup -1}.
  • The self-consistent semimicroscopic fully quantum approach developed recently for describing the structure of the inner crust of a neutron star within the Wigner-Seitz method is used to perform a systematic calculation of the properties of the system under study. Only the lowest layers of the crust in the vicinity of the point where a phase transition to a uniform state occurs are excluded from our consideration. Use is made of a realistic microscopic model that treats pairing in neutron matter with allowance for corrections of many-body theory to the Bardeen-Cooper-Schrieffer approximation.
  • A fully self-consistent model of the neutron star inner crust based upon models of the nucleonic equation of state at zero temperature is constructed. The results nearly match those of previous calculations of the inner crust given the same input equation of state. The extent to which the uncertainties in the symmetry energy, the compressibility, and the equation of state of low-density neutron matter affect the composition of the crust are examined. The composition and pressure of the crust is sensitive to the description of low-density neutron matter and the nuclear symmetry energy, and the latter dependence is nonmonotonic, givingmore » larger nuclei for moderate symmetry energies and smaller nuclei for more extreme symmetry energies. Future nuclear experiments may help constrain the crust and future astrophysical observations may constrain the nuclear physics input.« less